主教(上)跨越不平等和较低的半计算随机现实
Bishop's (up)crossing inequality and lower semicomputable random reals revisited
Mikhail Andreev, Alexander Shen
arXiv
2025年11月12日
在本文中,我们提供了Barmpalias-Lewis-Pye结果的简单证明,即所有可计算增加的序列汇合到随机真实,以相同的速度(高达c+o(1)因子)收敛,并指出它立即遵循Bishop的交叉不平等。 我们还提供了这种不平等的简单推导。
In this paper we provide an easy proof of Barmpalias–Lewis-Pye result saying that all computable increasing sequences converging to random reals converge with the same speed (up to a c+o(1) factor) by noting that it immediately follows from Bishop's upcrossing inequality. We also provide a simple derivation of this inequality.